When a probability interval is a random set

ABSTRACT: Some uncertainties can be represented by random sets, while some others may be in the form of probability intervals. Even though random sets and probability intervals are defined differently, we may be able to represent a given probability interval as a unique random set when this probability interval satisfies some conditions. In this paper, we present these conditions which will check whether or not there is a unique random set expressing the same information as a given probability interval. We construct the random set when the conditions are satisfied. We also give examples of when a user should use a random set over a given probability interval.